It will be valid, it's just you weren't sort of momentum before or after an interaction (within certain limits obviously).

Giving wildly unrealistic numbers here consider particles A and B interacting. A has momentum somewhere in the range [5,6] and B is somewhere in [6,7]. If after interactioning A has momentum somewhere in [7,8] then you'd expect B to be in [4,5].

This is totally unrigorous and I half expect someone much more versed in QM to come along and correct me, but that's how I would reconcile the HUP and conservation of momentum.

Yes, that's right. There is in principle exact momentum conservation, but it are the uncertainties on the initial conditions which allow for the uncertainties on the final states. This can in fact be illustrated by using Bohmian mechanics where this is explicit.